170 GEOLOGY OF THE COMSTOCK LODE. 



Mei'e inspection also shows that 



XiI^X COS S, 



and the equation i-efeiTed to the inchned coordinates indicated will be 



y=Am-^""\ (4) 



By a proper selection of a unit and by removing the origin to a different 

 ]i()int on the a;-axis according to well known rules of analytical geometry,' 

 this equation may be reduced to the form shown in Fig. 6, 



y/rrlO-% (5) 



or 



x=z — \ogy; 



and the points on the curve may be directly plotted from a table of log- 

 arithms. The curve evidently cuts the v/-axis at the point where y is equal 



to the natural unit j, found as indicated in the foot-note. If the equation 

 were plotted on rectangular coordinates, would also be the constant value 



'As the CoMSTOCK Lode excites a lively interest in many localities where hooks of reference urn 

 rare, it may he a matter of convenience to some of my readers to give this reduction in fall. 

 Let 



/i = cos 3 log III, 



or 



10'' = m™''"'; 



then introducing; this value into (4), we have 



11 = A U)-'"'. 

 Let the oiij;!!! hi- tiai]s[iii.-,e(l on the x-asis hy a quantity a, yet to he determined; then 



!J=A 10"'*'*+"'=^ hi-'"' lU-'"^. 

 Now let 



h 

 The iiiliipiliH liiiii of this value brings lliu equation to the lorm 



liecause ior the chosen value of n 



,j = \vr 



